Hard Surface modelling is possibly the most challenging discipline within 3D CAD – and the most rewarding, once you’ve got the way of it…

With a bit of surfacing theory you too can relish meeting the challenge with Autodesk Inventor!

G2 = Continuity + Tangency + Curvature

The coolest racing car ever bar none – Jason’s Spacemobile from ‘G-Force Battle of the planets. By weird coincidence it’s number is G-2, which I did not recall when I started writing this article!

In real life, racing car drivers aren’t able to execute 90 degree turns , with or without the aid of grappling hooks! To minimise breaking and maximise speed through a corner, racing driver takes the ‘racing line’ – the smoothest curve through the corner that the width of the road will allow.

G2 continuity adds another order (condition) that must match across our pair of curves. Our curves must now touch, be tangent with each other – and have the same curvature, at the point where they touch.

Technically – this means that our input geometry must be now be curved as well. Straight lines have no curvature (or Infinite curvature, depending on your point of view) so a pair of inputs containing a straight line can’t meet G2 conditions*.

Arc’s have a constant curvature. A pair of tangent arcs with the same curvature where they touch would either form a circle – or an ‘S’ shape. Abandoning Lines and Arcs of course means that Splines become really important input geometry from G2+ surfaces.

The easiest way to demonstrate equal curvature is to use 2D curvature comb analysis (right click on any curved 2D geometry to turn this on). The ‘porcupine spines’ in the image are heading in the same direction where the two curves meet -indicating that they are tangent. The spines are also the same length, indicating that the curves have equal radius at the contact point.

In real terms, G2 continuity means that the relationship between your two surfaces will be very smooth. In most cases this will be all you need to achieve to get a great result. However, for those rare occasions when ‘good enough – isn’t good enough’, we can introduce a further order of continuity.